NOTE ON SPECTRAL GAP AND WEIGHTED POINCARÉ INEQUALITIES FOR SOME ONE-DIMENSIONAL DIFFUSIONS.

BONNEFONT, MICHEL; JOULIN, ALDÉRIC; YUTAO MA

We present some classical and weighted Poincaré inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric probability measures in dimension larger than 2. Our strategy is based on two main ingredients: on the one hand, the optimal constant in the desired weighted Poincaré inequality has to be rewritten as the spectral gap of a convenient Markovian diffusion operator, and on the other hand we use a recent result given by the two first authors, which allows to estimate precisely this spectral gap. In particular we are able to capture its exact value for some examples.

POINCARE series; VARIATIONAL inequalities (Mathematics); PROBABILITY measures; RIEMANNIAN manifolds; RIEMANNIAN metric

ESAIM: Probability & Statistics, 2016, Vol 20, p18

1292-8100

Academic Journal

10.1051/ps/2015019